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Journal articles on the topic 'Riemannian spaces'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Kath, I. "Pseudo-RiemannianT-duals of compact Riemannian homogeneous spaces." Transformation Groups 5, no. 2 (2000): 157–79. http://dx.doi.org/10.1007/bf01236467.

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2

Aleksandrov, A. D., V. N. Berestovskii, and I. G. Nikolaev. "Generalized Riemannian spaces." Russian Mathematical Surveys 41, no. 3 (1986): 1–54. http://dx.doi.org/10.1070/rm1986v041n03abeh003311.

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3

Kantor, I. L., A. I. Sirota, and A. S. Solodovnikov. "Bisymmetric Riemannian spaces." Izvestiya: Mathematics 59, no. 5 (1995): 963–70. http://dx.doi.org/10.1070/im1995v059n05abeh000043.

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4

Plaut, Conrad. "Almost Riemannian spaces." Journal of Differential Geometry 34, no. 2 (1991): 515–37. http://dx.doi.org/10.4310/jdg/1214447219.

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5

Berezovski, Volodymyr, Yevhen Cherevko, and Lenka Rýparová. "Conformal and Geodesic Mappings onto Some Special Spaces." Mathematics 7, no. 8 (2019): 664. http://dx.doi.org/10.3390/math7080664.

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In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine conne

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6

Minčić, S. M., and L. S. Velimirović. "On generalized Riemannian spaces containing Riemannian subspaces." Russian Mathematics 51, no. 11 (2007): 30–34. http://dx.doi.org/10.3103/s1066369x07110047.

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7

Petrović, Miloš Z., Mića S. Stanković, and Patrik Peška. "On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces." Mathematics 7, no. 7 (2019): 626. http://dx.doi.org/10.3390/math7070626.

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We consider conformal and concircular mappings of Eisenhart’s generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart’s generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart’s generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano’s tensor of concircular curvature in Eisenhart symmetric spaces of various kinds.

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8

Burstall, Francis, Simone Gutt, and John Rawnsley. "Twistor spaces for Riemannian symmetric spaces." Mathematische Annalen 295, no. 1 (1993): 729–43. http://dx.doi.org/10.1007/bf01444914.

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9

Popov, Vladimir A. "Locally Isometric Riemannian Analytic Spaces." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 4-1 (216-1) (December 28, 2022): 55–64. http://dx.doi.org/10.18522/1026-2237-2022-4-1-55-64.

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Classes of locally isometric Riemannian analytic manifolds are studied. A generalization of the concept of completeness is given. We consider the Lie algebra 𝔤 of all Killing vector fields of a Riemannian analytic manifold, its stationary subalgebra 𝔥 the simply connected Lie group 𝐺 corresponding to the Lie algebra 𝔤, and the subgroup 𝐻 corresponding to the Lie subalgebra 𝔥. In the absence of a center in the algebra 𝔤 the concept of a quasi-complete (compressed) manifold is introduced. An oriented Riemannian analytic manifold whose vector field algebra has zero center is said to be quasi-comp

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10

Jimenez, J. A. "Riemannian 4-Symmetric Spaces." Transactions of the American Mathematical Society 306, no. 2 (1988): 715. http://dx.doi.org/10.2307/2000819.

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11

Hervik, Sigbjørn, and Alan Coley. "Pseudo-Riemannian VSI spaces." Classical and Quantum Gravity 28, no. 1 (2010): 015008. http://dx.doi.org/10.1088/0264-9381/28/1/015008.

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12

Jim{énez, J. A. "Riemannian $4$-symmetric spaces." Transactions of the American Mathematical Society 306, no. 2 (1988): 715. http://dx.doi.org/10.1090/s0002-9947-1988-0933314-6.

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13

Smolentsev, N. K. "Spaces of Riemannian metrics." Journal of Mathematical Sciences 142, no. 5 (2007): 2436–519. http://dx.doi.org/10.1007/s10958-007-0185-3.

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14

Федченко, Юлія Степанівна, and Олександр Васильович Лесечко. "Special semi-reducible pseudo-Riemannian spaces." Proceedings of the International Geometry Center 14, no. 1 (2021): 48–59. http://dx.doi.org/10.15673/tmgc.v14i1.1940.

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 The paper contains necessary conditions allowing to reduce matrix tensors of pseudo-Riemannian spaces to special forms called semi-reducible, under assumption that the tensor defining tensor characteristic of semireducibility spaces, is idempotent. The tensor characteristic is reduced to the spaces of constant curvature, Ricci-symmetric spaces and conformally flat pseudo-Riemannian spaces.  The obtained results can be applied for construction of examples of spaces belonging to special types of pseudo-Riemannian spaces.  The research is carried out locally i

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15

Kiosak, Volodymyr, Olexandr Lesechko, and Olexandr Latysh. "On geodesic mappings of symmetric pairs." Proceedings of the International Geometry Center 15, no. 3-4 (2023): 230–38. http://dx.doi.org/10.15673/tmgc.v15i3-4.2430.

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The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.

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16

Pihajoki, Pauli, Matias Mannerkoski, and Peter H. Johansson. "Barycentric interpolation on Riemannian and semi-Riemannian spaces." Monthly Notices of the Royal Astronomical Society 489, no. 3 (2019): 4161–69. http://dx.doi.org/10.1093/mnras/stz2447.

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ABSTRACT Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is a ubiquitous task in all of physics. In this work, we present a covariant generalization of the barycentric coordinates and the barycentric interpolation method for Riemannian and semi-Riemannian spaces of arbitrary dimension. We show that our new method preserves the linear accuracy property of barycentric interpolation in a coordinate-invariant sense. In addition, we show how the method can be used to interpolate constrained quantitie

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17

Fan, Xiaomeng, Zhi Gao, Yuwei Wu, Yunde Jia, and Mehrtash Harandi. "Learning a Gradient-free Riemannian Optimizer on Tangent Spaces." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (2021): 7377–84. http://dx.doi.org/10.1609/aaai.v35i8.16905.

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A principal way of addressing constrained optimization problems is to model them as problems on Riemannian manifolds. Recently, Riemannian meta-optimization provides a promising way for solving constrained optimization problems by learning optimizers on Riemannian manifolds in a data-driven fashion, making it possible to design task-specific constrained optimizers. A close look at the Riemannian meta-optimization reveals that learning optimizers on Riemannian manifolds needs to differentiate through the nonlinear Riemannian optimization, which is complex and computationally expensive. In this

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18

Lesechko, O., and T. Shevchenko. "PSEUDO-RIEMANNIAN SPACES WITH A SPECIAL RIEMANN TENSOR." Mechanics And Mathematical Methods 3, no. 1 (2021): 106–14. http://dx.doi.org/10.31650/2618-0650-2021-3-1-106-114.

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The paper considers pseudo-Riemannian spaces, the Riemann tensor of which has a special structure. The structure of the Riemann tensor is given as a combination of special symmetric and obliquely symmetric tensors. Tensors are selected so that the results can be applied in the theory of geodetic mappings, the theory of holomorphic-projective mappings of Kähler spaces, as well as other problems arising in differential geometry and its application in general relativity, mechanics and other fields. Through the internal objects of pseudo-Riemannian space, others are determined, which are studied d

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19

Tuschmann, Wilderich. "Spaces and moduli spaces of Riemannian metrics." Frontiers of Mathematics in China 11, no. 5 (2016): 1335–43. http://dx.doi.org/10.1007/s11464-016-0576-1.

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20

Ho, Pei-Ming. "Riemannian Geometry on Quantum Spaces." International Journal of Modern Physics A 12, no. 05 (1997): 923–43. http://dx.doi.org/10.1142/s0217751x97000694.

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An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space.

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21

Lesechko, O., and A. Soloviov. "CONFORMALLY FLAT KÄHLERIAN SPACES." Researches in Mathematics and Mechanics 28, no. 1-2(41-42) (2023): 47–63. http://dx.doi.org/10.18524/2519-206x.2023.1-2(41-42).305257.

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We study the geometric properties of Kähler spaces admitting conformal mappings, other than homothetic mappings, to flat pseudo-Riemannian spaces. It is proved that there are no non-flat conformally flat Kählerian spaces with dimensions other than four. It is shown that four-dimensional conformally flat spaces can be embedded in six-dimensional flat pseudo-Riemannian spaces. An idempotent covariantly stable metric tensor is constructed in conformally flat Kählerian spaces and thus it is proved that these spaces are reduced pseudo-Riemannian spaces. The study is carried out locally, using tenso

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22

Ikawa, Osamu. "Equivariant minimal immersions of compact Riemannian homogeneous spaces into compact Riemannian homogeneous spaces." Tsukuba Journal of Mathematics 17, no. 1 (1993): 169–88. http://dx.doi.org/10.21099/tkbjm/1496162138.

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23

Andreeva, Tatiana A., Dmitry N. Oskorbin, and Evgeny D. Rodionov. "Investigation of conformally killing vector fields on 5-dimensional 2-symmetric lorentzian manifolds." Yugra State University Bulletin 60, no. 1 (2021): 17–22. http://dx.doi.org/10.17816/byusu20210117-22.

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Conformally Killing fields play an important role in the theory of Ricci solitons and also generate an important class of locally conformally homogeneous (pseudo) Riemannian manifolds. In the Riemannian case, V. V. Slavsky and E.D. Rodionov proved that such spaces are either conformally flat or conformally equivalent to locally homogeneous Riemannian manifolds. In the pseudo-Riemannian case, the question of their structure remains open. Pseudo-Riemannian symmetric spaces of order k, where k 2, play an important role in research in pseudo-Riemannian geometry. Currently, they have been investiga

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24

GÜLBAHAR, Mehmet, Erol KILIÇ, and Sadık KELEŞ. "Some Notes Concerning Riemannian Submersions and Riemannian Homogenous Spaces." International Electronic Journal of Geometry 12, no. 1 (2019): 116–25. http://dx.doi.org/10.36890/iejg.545856.

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25

Perales, Raquel. "Convergence of manifolds and metric spaces with boundary." Journal of Topology and Analysis 12, no. 03 (2018): 735–74. http://dx.doi.org/10.1142/s1793525319500638.

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We study sequences of oriented Riemannian manifolds with boundary and, more generally, integral current spaces and metric spaces with boundary. We prove theorems demonstrating when the Gromov–Hausdorff (GH) and Sormani–Wenger Intrinsic Flat (SWIF) limits of sequences of such metric spaces agree. Thus in particular the limit spaces are countably [Formula: see text] rectifiable spaces. From these theorems we derive compactness theorems for sequences of Riemannian manifolds with boundary where both the GH and SWIF limits agree. For sequences of Riemannian manifolds with boundary we only require n

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26

Stankovic, Vladislava. "Certain properties of generalized Einstein spaces." Filomat 32, no. 13 (2018): 4803–10. http://dx.doi.org/10.2298/fil1813803s.

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In the present paper are introduced generalized Einstein spaces. Einstein type tensors are represented in the generalized Einstein spaces. Some relations of Einstein type tensors of the first and the second kind in the generalized Riemannian space are obtained. Also, geodesic mappings of T-connected generalized Einstein spaces onto Riemannian space are considered.

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27

Mashimo, Katsuya, and Koji Tojo. "Circles in Riemannian symmetric spaces." Kodai Mathematical Journal 22, no. 1 (1999): 1–14. http://dx.doi.org/10.2996/kmj/1138043984.

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28

OTHMAN, S. I., and V. ANANDAM. "Biharmonic classification of Riemannian spaces." Hokkaido Mathematical Journal 32, no. 3 (2003): 457–71. http://dx.doi.org/10.14492/hokmj/1350659151.

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29

Ferrando, Joan Josep, and Juan Antonio Sáez. "Homogeneous three-dimensional Riemannian spaces." Classical and Quantum Gravity 37, no. 18 (2020): 185011. http://dx.doi.org/10.1088/1361-6382/ab9880.

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30

Carbó-Dorca, Ramon. "Riemannian three dimensional molecular spaces." Journal of Mathematical Chemistry 44, no. 1 (2007): 286–300. http://dx.doi.org/10.1007/s10910-007-9315-x.

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31

Roxburgh, Ian W. "Finsler spaces with Riemannian geodesics." General Relativity and Gravitation 23, no. 9 (1991): 1071–80. http://dx.doi.org/10.1007/bf00756867.

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32

Ovando, Gabriela P. "Naturally reductive pseudo-Riemannian spaces." Journal of Geometry and Physics 61, no. 1 (2011): 157–71. http://dx.doi.org/10.1016/j.geomphys.2010.09.011.

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33

Kowalski, Old?ich, and Masami Sekizawa. "On 3-dimensional Riemannian ?-spaces." Monatshefte f�r Mathematik 103, no. 4 (1987): 303–20. http://dx.doi.org/10.1007/bf01318071.

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34

Hojman, Sergio A., and Darío Núñez. "Affine collineations in Riemannian spaces." Journal of Mathematical Physics 32, no. 1 (1991): 234–38. http://dx.doi.org/10.1063/1.529123.

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35

Hervik, Sigbjørn. "Pseudo-Riemannian VSI spaces II." Classical and Quantum Gravity 29, no. 9 (2012): 095011. http://dx.doi.org/10.1088/0264-9381/29/9/095011.

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36

Gittel, Hans-Peter, Jacek Jezierski, Jerzy Kijowski, and Szymon Łęski. "Rigid spheres in Riemannian spaces." Classical and Quantum Gravity 30, no. 17 (2013): 175010. http://dx.doi.org/10.1088/0264-9381/30/17/175010.

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37

Binh, T. Q. "On weakly symmetric Riemannian spaces." Publicationes Mathematicae Debrecen 42, no. 1-2 (1993): 103–7. http://dx.doi.org/10.5486/pmd.1993.1281.

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38

De, U. C., and Somnath Bandyopadhyay. "On weakly symmetric Riemannian spaces." Publicationes Mathematicae Debrecen 54, no. 3-4 (1999): 377–81. http://dx.doi.org/10.5486/pmd.1999.1999.

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39

Kiosak, V., L. Kusik, and V. Isaiev. "Geodesic Ricci-symmetric pseudo-Riemannian spaces." Proceedings of the International Geometry Center 15, no. 2 (2022): 109–19. http://dx.doi.org/10.15673/tmgc.v15i2.2224.

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We introduced special pseudo-Riemannian spaces, called geodesic A-symmetric spaces, into consideration. It is proven that there are no geodesic symmetric spaces and no geodesic Ricci symmetric spaces, which differ from spaces of constant curvature and Einstein spaces respectively. The research is carried out locally, by tensor methods, without any limitations imposed on a metric and a sign.

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40

Berndt, Jürgen, and Carlos Olmos. "On the index of symmetric spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 737 (2018): 33–48. http://dx.doi.org/10.1515/crelle-2015-0060.

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AbstractLetMbe an irreducible Riemannian symmetric space. The index ofMis the minimal codimension of a (nontrivial) totally geodesic submanifold ofM. We prove that the index is bounded from below by the rank of the symmetric space. We also classify the irreducible Riemannian symmetric spaces whose index is less than or equal to 3.

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41

BUCKLEY, S. M., K. FALK, and D. J. WRAITH. "PTOLEMAIC SPACES AND CAT(0)." Glasgow Mathematical Journal 51, no. 2 (2009): 301–14. http://dx.doi.org/10.1017/s0017089509004984.

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AbstractWe consider Ptolemy's inequality in a metric space setting. It is not hard to see that CAT(0) spaces satisfy this inequality. Although the converse is not true in full generality, we show that if our Ptolemaic space is either a Riemannian or Finsler manifold, then it must also be CAT(0). Ptolemy's inequality is closely related to inversions of metric spaces. We exploit this link to establish a new characterization of Euclidean space amongst all Riemannian manifolds.

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42

LE, HUILING, and DENNIS BARDEN. "ON SIMPLEX SHAPE SPACES." Journal of the London Mathematical Society 64, no. 2 (2001): 501–12. http://dx.doi.org/10.1112/s0024610701002332.

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The right-invariant Riemannian metric on simplex shape spaces in fact makes them particular Riemannian symmetric spaces of non-compact type. In the paper, the general properties of such symmetric spaces are made explicit for simplex shape spaces. In particular, a global matrix coordinate representation is suggested, with respect to which several geometric features, important for shape analysis, have simple and easily computable expressions. As a typical application, it is shown how to locate the Fréchet means of a class of probability measures on the simplex shape spaces, a result analogous to

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43

Morawo, Monsuru A., Hina A. D., and Azeez K. Y. "Gromov - Hausdorff Dimension and Measure of Separable Metric Spaces." Asian Journal of Science, Technology, Engineering, and Art 3, no. 2 (2025): 488–96. https://doi.org/10.58578/ajstea.v3i2.5206.

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44

Chongshan, Luo. "On concircular transformations in Riemannian spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 2 (1986): 218–25. http://dx.doi.org/10.1017/s1446788700027191.

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AbstractThis paper introduces a tensor that contains the Riemannian curvature tensor and the conformal curvature tensor as special examples in the Riemannian space (Mn, g), and by using this tensor we define C-semi-symmetric space. In this paper, we have the following main result: if there is a non-trivial concircular transformation between two C-semi-symmetric spaces, then both spaces are of quasi-constant curvature.

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45

Grove, Karsten. "Book Review: Metric structures for Riemannian and non-Riemannian spaces." Bulletin of the American Mathematical Society 38, no. 03 (2001): 353–64. http://dx.doi.org/10.1090/s0273-0979-01-00904-1.

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46

Mikes, Josef, and Lenka Rýparová. "Rotary mappings of spaces with affine connection." Filomat 33, no. 4 (2019): 1147–52. http://dx.doi.org/10.2298/fil1904147m.

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This paper concerns with rotary mappings of two-dimensional spaces with an affine connection onto (pseudo-) Riemannian spaces. The results obtained in the theory of rotary mappings are further developed. We prove that any (pseudo-) Riemannian space admits rotary mapping. There are also presented certain properties from which yields the existence of these rotary mappings.

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47

Шевченко, Тетяна Iванiвна, Тетяна Сергіївна Спічак, and Дмитро Миколайович Дойков. "On conformally reducible pseudo-Riemannian spaces." Proceedings of the International Geometry Center 14, no. 2 (2021): 154–63. http://dx.doi.org/10.15673/tmgc.v14i2.2097.

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 The present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried

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48

Álvarez, López Jesús Antonio, Lijó Ramón Barral, and Alberto Candel. "A Universal Riemannian foliated space." Topology and its Applications 198 (June 5, 2016): 47–85. https://doi.org/10.5281/zenodo.10644182.

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It is proved that the isometry classes of pointed connected complete Riemannian <em>n</em>-manifolds form a Polish space with the topology described by the C∞ convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifold. The locally non-periodic manifolds define an open dense subspace which becomes a C∞ foliated space with the restriction of the canonical partition. Its leaves without holonomy form the subspace defined by the non-periodic manifolds. Moreover the leaves have a natural Riemannian stru

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49

Chen, Bang-Yen, and Sharief Deshmukh. "Some results about concircular vector fields on Riemannian manifolds." Filomat 34, no. 3 (2020): 835–42. http://dx.doi.org/10.2298/fil2003835c.

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In this article, we show that the presence of a concircular vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian and Kaehler manifolds. More precisely, we find new geometrical characterizations of spheres, Euclidean spaces as well as of complex Euclidean spaces using non-trivial concircular vector fields.

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50

Haesen, Stefan, Miroslava Petrović-torgašev, and Leopold Verstraelen. "On Thurston's Geometrical Space Form Problem: On Quasi Space Forms." International Electronic Journal of Geometry 17, no. 1 (2024): 232–44. http://dx.doi.org/10.36890/iejg.1466330.

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A proposal is made for what may well be the most elementary Riemannian spaces which are homogeneous but not isotropic. In other words: a proposal is made for what may well be the nicest symmetric spaces beyond the real space forms, that is, beyond the Riemannian spaces which are homogeneous and isotropic. The above qualification of ‘’nicest symmetric spaces” finds a justification in that, together with the real space forms, these spaces are most natural with respect to the importance in human vision of our ability to readily recognise conformal things and in that these spaces are most natural

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